Answer
$x=5$
Work Step by Step
The given equation is
$\Rightarrow 216^{x}=6^{x+10}$
Rewrite $216$ as $6^3$.
$\Rightarrow (6^3)^{x}=6^{x+10}$
Use $(a^n)^m=a^{n\cdot m}$
$\Rightarrow 6^{3x}=6^{x+10}$
Equate the exponents.
$\Rightarrow 3x=x+10$
Subtract $x$ from each side.
$\Rightarrow 3x-x=x+10-x$
Simplify.
$\Rightarrow 2x=10$
Divide each side by $2$.
$\Rightarrow \frac{2x}{2}=\frac{10}{2}$
Simplify.
$\Rightarrow x=5$
Check: $(x=5)$
$\Rightarrow 216^{x}=6^{x+10}$
$\Rightarrow 216^{5}=6^{5+10}$
$\Rightarrow 216^{5}=6^{15}$
$\Rightarrow470184984576=470184984576$
True.
Hence, the solution is $x=5$.
